Strategic Knowledge of the Past in Quantum Cryptography

Abstract

We propose an epistemic strategy logic with future and past time operators, called \(\text {SLKP}\), for Strategy Logic with Knowledge of the Past. With \(\text {SLKP}\) we can model mutually observed moves/actions in strategic contexts. In a semantic game, agents may completely or partially observe other agents’ moves, their moves may depend on their knowledge of other players’ strategies, and their knowledge may depend on the history of their own or other’s moves. The logic \(\text {SLKP}\) also allows us to describe temporal properties involving past, future, and composed tenses such as future perfect or counterfactual assertions. We illustrate SLKP by formalising the quantum cryptography protocol BB84, with the purpose to initiate an integrated epistemic and strategic treatment of agent interactions in quantum systems.